Jennifer J. Zhao
Department of Mathematics and Statistics
University of Michigan at Dearborn
Dearborn, MI 48128-1491, USA
We investigate the use of a fourth order compact finite difference scheme for solving an one dimensional heat transport equation at the microscale. The fourth order compact scheme is used with a Crank-Nicholson type integrator by introducing an intermediate function for the heat transport equation. The new scheme is proved to be unconditionally stable with respect to initial values. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second order spatial discretization. It is shown that the new scheme is computationally more efficient and more accurate than the second order scheme.
Mathematics Subject Classification: 65M06, 65N12.